Thermal stress hysteresis and stress relaxation in an epoxy film

Abstract

Thermal cycling of an epoxy coating on silicon through the glass transition temperature (T _g) revealed a large stress hysteresis on the first thermal cycle through T _g and a change in the stress–temperature slope at T _g resulting from the change in the epoxy elastic properties due to the glass transition. This stress hysteresis was not observed on subsequent thermal cycles through T _g. However, after the coating was annealed (aged) below T _g (for hours or longer)—during which the stress relaxed exponentially with time—the stress hysteresis returned. The magnitude of stress hysteresis, on cycling through T _g, was found to correlate to the magnitude of long-time relaxation that occurred during annealing at temperatures below T _g.

Appendix A: Non-linear deformation analysis

The use of Eq. 1 requires that the strains and rotations in the system be infinitesimally small. This requirement was examined using the analysis of Freund et al. [27], who showed that non-linear deformation effects can be avoided if the dimensionless parameters S or K are less than 0.3–0.4 or 0.2, respectively:

$$ S = 1.5\varepsilon _{\hbox{m}} R^2 t\frac{{(1 - \nu _{\hbox{s}} )E_{\hbox{f}} }} {{(1 - \nu )E_{\hbox{s}} t_{\hbox{s}}^3 }} $$

(A1)

and

$$ K = 0.25R^2 \frac{{\Delta \kappa }} {{t_{\hbox{s}} }}, $$

(A2)

where ε _m is the imposed thermal mismatch strain, R is the sample radius (50 mm), E _f is the film Young’s Modulus, and ν is the film Poisson’s Ratio. Since the film mechanical properties are not known, the parameter K was evaluated using the largest change in curvature observed over the course of the experiment, Δκ = 0.02 m⁻¹, to be K = 0.016. As K < 0.2, non-linear deformations were not considered.